I'm working a lot with Google ads and when I tested ChatGPT it was just not able to limit their output to a certain number of characters. It always failed to give at max 90 characters. When I tell it, that it used more, it apologizes, gives another output and makes the same mistake.
You are the only one that got the problem. I was wondering why even the author of the article got the problem wrong.
A perfect logican always needs a 100% chance for stopping the game. Each message could either be:
a) the exact same strategy
b) the same strategy with a small variance that is also reasonable
c) a completely reasonable other strategy
d) just a color
e) waiting or something unrelated to the problem itself
The problem is that every proposal of a-e could get matched with something a-e that ruins it.
Examples:
1. I say just a color, they say just a color. You stay by the color they also stay, you decide to switch they also do it at the same time.
2. You propose something to confirm, so did they and we are back at 1.
3. You decide to do something random and they also decide to do something random with the same outcome
Since you are both perfect logical, you will realize that, making any try obsolete.
So you could try to get to know each other and just chat to something unrelated but there is still the problem that they could exactly mirror your messages again.
So you both come to the conclusion that there is no 100% strategy. You could now decide that you should continue playing the game forever or decide that a strategy with less than 100% is good enough.
Both have etablished now that using a meta strategy to agree on something is just a waste of time, because of a-e and we can just stay on the main layer. Repeating the color is also useless because the other might have the same strategy. So the only solution would be to announce just random colors and as soon as they match we end the game and are free. Theoretically they never have to match so the game could just go forever (hence it's not 100%).